At which site does the repressor bind in the $Lac$ operon?

The lac operon consists of

An organism is able to survive on a culture medium containing nutrient $A$ through an enzyme-catalyzed process: $A \xrightarrow{X} B \xrightarrow{Y} C$. $A$ mutant organism fails to survive on this medium. However,it grows when nutrient $B$ is added to the medium. Which gene of this mutant is defective?

In the $lac$ operon concept of gene expression,allolactose acts as:

Assertion $(A):$ Regulation of $lac$ operon by repressor is referred to as negative regulation.
Reason $(R):$ Repressor protein binds to the operator region and prevents $\text{RNA}$ polymerase from transcribing the operon.

What does '$4$' represent in the given figure?